I'm looking to upgrade at least the current (stock) graphics card that came with this PC. It's a cheap Nvidia GT620 which is nothing special but obviously playing games for Dolphin (in addition to some PC games) on the higher settings, well, it struggles. It runs well on native and sometimes 2x res just fine at 60 FPS, but I want to upgrade and get something better. I'm looking to spend a couple hundred bucks or so, but nothing crazy like in the 300 or 400 range; for a PC and mostly limited to emulation and the odd PC game here and there, that seems a bit much to me.

Looks like you bought some OEM computer. Could you tell us what exact brand and model it is?
If you're going to change components, you might have to change the PSU (Power supply) too since the GT620 is a very low-end card meant for HTPCs. The PSU is likely skimped on to just be able to power that specific configuration. But we'll know more after you provide us more information on your PC.

The GTX 660 is a good choice for what you're aiming for. What's the price you're getting it at and from what store?

I haven't had it apart yet, so I'm not clear on what it's power supply unit may be. I had heard before that the PSU may need replacing as well.

As for the computer itself, yeah I bought it off the rack a few months ago and it works surprisingly well for all the emulation and games I run on it. It's an Acer Aspire MC605 with an Ivy Bridge 77W chipset, Intel i7 Core 3770k @ 3.40 GHz. It has 6 GB of RAM. I have CPU-Z open at the moment, so if there's anything else you need to know, let me know!

And yes, the graphics card was not meant for emulation on higher scaled resolutions. At all. I'm amazed it runs as well as it does. I've seen the card running as hot as 77 C once (on very high settings), but it usually doesn't go over 60 or so, if I'm running a game on Dolphin or PCSX2.

I am looking at the GTX 660 ti. It sounds great and it wasn't all that expensive now either, so I thought, why not? But I need to make sure everything is all prepped beforehand.

a 300 W will never fly for a 660 ti. Either get a nice reviewed 800 watt or pay great attention to the 12 volt rail. The GTX 660 has a max 140W draw, which divided by 12V gives a little under 12A requirement. So you can go much lower then 800 but makes sure the 12volt rail is around 12 amps or better.

Seems I'm seeing mixed review on the spec, some claim it needs 24amp per rail. Best to be safe in that case unless someone here can confirm.

a picture on the 660 EVGA box shows:http://i.imgur.com/uy10hoV.jpg Img way to big to post in here.
This confirms it. You need a max of 24 that is 12 per connector. This card needs two connection so when buying a PSU get one that has more then 24 amp per 12v rail. Sometime they show you per connector, other ties it per rail. So it can get confusing.

Also my experience of OEM cases is that they don't have the ability to let out hot air, which a powerful GPU will release, so you may need to replace that, too.

OS: Windows 10 64 bit Professional
CPU: Intel i5 4670K @3.4GHz... for now @4.6GHz with a quick and dirty (yet stable) OC. May get faster in a bit before the end of time.
RAM: 16GB (Down from 24 GB after some was given to siblings)
GPU: Radeon Vega 56

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